The most common way is to first break up vectors into x and y parts, like this: The vector a is broken up into the two vectors a x and a y (We see later how to do this.) Adding Vectors. We can then add vectors by adding the x parts and adding the y parts: The vector (8, 13) and the vector (26, 7) add up to the vector (34, 20)

Enter values into Magnitude and Angle ... or X and Y. It will do conversions and sum up the vectors. Learn about Vectors and Dot Products.

A vector has magnitude (how long it is) and direction: Here are two vectors: They can be multiplied using the "Dot Product" (also see Cross Product). Calculating. The Dot Product is written using a central dot: a · b This means the Dot Product of a and b. We can calculate the Dot Product of two vectors this way: a · b = |a| × |b| × cos(θ ...

Notice how we multiply a matrix by a vector and get the same result as when we multiply a scalar (just a number) by that vector. How do we find these eigen things? We start by finding the eigenvalue .

The Cross Product gives a vector answer, and is sometimes called the vector product. But there is also the Dot Product which gives a scalar (ordinary number) answer, and is sometimes called the scalar product .

A vector is a list of numbers (can be in a row or column), A matrix is an array of numbers (one or more rows, one or more columns). In fact a vector is also a matrix! Because a matrix can have just one row or one column. So the rules that work for matrices also work for vectors.

The bra-ket notation is a simple way to refer to a vector with complex elements, any number of dimensions, that represents one state in a state space. The probability of any state equals the magnitude of its vector squared.

Example: does y = 1/x have Diagonal Symmetry? Start with: y = 1/x. Try swapping y with x: x = 1/ y . Now rearrange that: multiply both sides by y: xy = 1. Then divide both sides by x: y = 1/x. And we have the original equation. They are the same. So y = 1/x has Diagonal Symmetry

Here we show that the vector a is made up of 2 "x" unit vectors and 1.3 "y" unit vectors. In 3 Dimensions Likewise we can use unit vectors in three (or more!) dimensions:

This page is about second order differential equations of this type ... d2ydx2 P(x)dydx Q(x)y = f(x) ... where P(x), Q(x) and f(x) are functions of x.